Just as ∇⋅B=0 allows us to express B as the curl of a vector potential (B=∇×A), so ∇⋅A=0 permits us to write A itself as the curl of a "higher" potential: A=∇×W. (And this hierarchy can be extended ad infinitum.)
(a) Find the general formula for W (as an integral over B), which holds when B→0 at ∞.
(b) Determine W for the case of a uniform magnetic field B. [Hint: see Prob. 5.25.]
(c) Find W inside and outside an infinite solenoid. [Hint: see Ex. 5.12.]